ON A NEW ELLIPTIC ANALYSER. 199 minor to the major axis, and about the thousandth part of an undulation in the determination of the retardation. On account of the accuracy with which the retardation is determined, and the largeness of the chromatic variations to which it is subject, the instrument may be considered as determining, not only the elements of the ellipse described, but also the refrangibi-lity of the light employed, or its length of wave, which corresponds to the refrangibility. The author stated that the error of the thousandth part of an undulation, to which the determination of the retardation was subject, corresponded to an error of only the twentieth or thirtieth part of the interval between the fixed lines D and E of Fraunhofer. [Apart from the details of construction of the instrument, the distinctive feature of the method of observation here described consists in regarding the retardation due to the plate as an unknown quantity, which is eliminated by the method of observation. The author was not aware when the paper was communicated to the British Association that he had been anticipated in this by Mac Cullagh. (See Proceedings of the Royal Irish Academy, Vol. II. p. 384, or Collected works of Mac Cidlagh, p. 239.) Mac Cul-lagh's actual observations were made with a Fresnel's Rhomb, not a retarding plate, but of course the principle is the same in the two cases. In the use of the instrument here described, the observer has got to extinguish the transmitted light, or in case the incident light used be not homogeneous, to reduce it to a minimum, by the alternate employment of the two angular motions of which such an instrument must be susceptible. In designing the instrument, the choice of the two angular motions which shall be independent of each other is not altogether a matter of indifference. It might have been constructed either (a) so that the Nicol's prism and the retarding plate should rotate independently, or (6) so that the prism and plate should rotate together and the prism independently, or (c) so that the prism and plate should rotate together and the plate independently. It is evidently desirable that in adjusting one of the rotations so as to reduce the intensity of the transmitted light to a minimum the adjustment of the other should not be much put out.